Questions: Evaluate the algebraic expression at (x=-7, y=4) and simplify your answer. [5 x^2-5 y^2-2]

Solution Steps

To solve the given expression \(5x^2 - 5y^2 - 2\) at \(x = -7\) and \(y = 4\), we need to substitute the values of \(x\) and \(y\) into the expression and then simplify the result.

We start with the expression \(5x^2 - 5y^2 - 2\). We substitute \(x = -7\) and \(y = 4\) into the expression:

\[ 5(-7)^2 - 5(4)^2 - 2 \]

Next, we calculate the squares of the substituted values:

\[ (-7)^2 = 49 \quad \text{and} \quad (4)^2 = 16 \]

Now we substitute these squared values back into the expression:

\[ 5(49) - 5(16) - 2 \]

We perform the multiplication:

\[ 5(49) = 245 \quad \text{and} \quad 5(16) = 80 \]

Now we simplify the expression:

\[ 245 - 80 - 2 \]

Finally, we perform the subtraction:

\[ 245 - 80 = 165 \] \[ 165 - 2 = 163 \]

Final Answer